Optimal stopping and perpetual options for Lévy processes

Ernesto Mordecki ()
Additional contact information
Ernesto Mordecki: Centro de Matemática, Facultad de Ciencias, Universidad de la República, Iguá 4225, CP 11400, Montevideo, Uruguay , URL:http://www.cmat.edu.uy/&mtilde;ordecki Manuscript

Finance and Stochastics, 2002, vol. 6, issue 4, 473-493

Abstract: Consider a model of a financial market with a stock driven by a Lévy process and constant interest rate. A closed formula for prices of perpetual American call options in terms of the overall supremum of the Lévy process, and a corresponding closed formula for perpetual American put options involving the infimum of the after-mentioned process are obtained. As a direct application of the previous results, a Black-Scholes type formula is given. Also as a consequence, simple explicit formulas for prices of call options are obtained for a Lévy process with positive mixed-exponential and arbitrary negative jumps. In the case of put options, similar simple formulas are obtained under the condition of negative mixed-exponential and arbitrary positive jumps. Risk-neutral valuation is discussed and a simple jump-diffusion model is chosen to illustrate the results.

Keywords: Optimal stopping; Lévy processes; mixtures of exponential distributions; American options; jump-diffusion models (search for similar items in EconPapers)
JEL-codes: G12 (search for similar items in EconPapers)
Date: 2002-08-19
Note: received: June 2000; final version received: November 2001
References: Add references at CitEc
Citations: View citations in EconPapers (71)

Downloads: (external link)
http://link.springer.de/link/service/journals/00780/papers/2006004/20060473.pdf (application/pdf)
Access to the full text of the articles in this series is restricted

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:finsto:v:6:y:2002:i:4:p:473-493

Ordering information: This journal article can be ordered from
http://www.springer. ... ance/journal/780/PS2

Access Statistics for this article

Finance and Stochastics is currently edited by M. Schweizer

More articles in Finance and Stochastics from Springer
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().